Bayes' Rule With Python

"An accessible introduction to Bayesian analysis for those with little mathematical experience."
Journal of the Royal Statistical Society, 2015.

"An excellent book ... highly recommended. "
CHOICE: Academic Reviews Online, February 2014.

"Short, interesting, and very easy to read, Bayes' Rule serves as an excellent primer for students and professionals ... "
Top Ten Math Books On Bayesian Analysis, July 2014.

"An excellent first step for readers with little background in the topic. "
Computing Reviews, June 2014.

"A crackingly clear tutorial for beginners. Exactly the sort of book required for those taking their first steps in Bayesian analysis."
Dr Paul A. Warren.
School of Psychological Sciences, University of Manchester.

"This book is short and eminently readable. It introduces the Bayesian approach to addressing statistical issues without using any advanced mathematics, which should make it accessible to students from a wide range of backgrounds, including biological and social sciences."
Dr Devinder Sivia.
Lecturer in Mathematics, St John's College, Oxford University, and author of Data Analysis: A Bayesian Tutorial.

"For those with a limited mathematical background, Stone's book provides an ideal introduction to the main concepts of Bayesian analysis. "
Dr Peter M Lee.
Department of Mathematics, University of York. Author of Bayesian Statistics: An Introduction.

"Bayesian analysis involves concepts which can be hard for the uninitiated to grasp. Stone's patient pedagogy and gentle examples convey these concepts with uncommon lucidity. "
Dr Charles Fox.
Department of Computer Science, University of Sheffield.

Preface

1 An Introduction to Bayes' Rule
1.1 Example 1: Poxy Diseases
1.2 Example 2: Forkandles
1.3 Example 3: Flipping Coins
1.4 Example 4: Light Craters
1.5 Forward and Inverse Probability

2 Bayes' Rule in Pictures
2.1 Random Variables
2.2 The Rules of Probability
2.3 Random Variables and Coin Flips
2.4 Joint Probability and Coin Flips
2.5 Probability As Geometric Area
2.6 Bayes' Rule From Venn Diagrams
2.7 Bayes' Rule and the Medical Test

3 Discrete Parameter Values
3.1 Joint Probability Functions
3.2 Patient Questions
3.3 Deriving Bayes' Rule
3.4 Using Bayes' Rule
3.5 Bayes' Rule and the Joint Distribution

4 Continuous Parameter Values
4.1 A Continuous Likelihood Function
4.2 A Binomial Prior Probability Density Function
4.3 A Posterior Probability Density Function
4.4 A Uniform Prior Probability Density Function
4.5 MAP Estimates Are Not Aected By Constants
4.6 Finding the MAP Estimate Analytically
4.7 Evolution of the Posterior
4.8 Reference Priors
4.9 Loss Functions

5 Gaussian Parameter Estimation
5.1 The Gaussian Distribution
5.2 Estimating the Population Mean
5.3 Error Bars for Gaussian Distributions
5.4 Regression as Parameter Estimation

6 A Bird's-Eye View of Bayes' Rule
6.1 Joint Gaussian Distributions
6.2 A Bird's-Eye View of Joint Distributions
6.3 A Bird's-Eye View of Bayes' Rule
6.4 Slicing Through Joint Distributions
6.5 Statistical Independence

7 Bayesian Wars
7.1 The Nature of Probability
7.2 Subjective Probability
7.3 Bayesian Wars
7.4 A Very Short History of Bayes' Rule

Further Reading

Appendices
A Glossary
B Mathematical Symbols
C The Rules of Probability
D Probability Density Functions
E The Binomial
F The Gaussian
G Least-Squares Estimation
H Reference Priors
I MatLab Code

References

Index